Pertanyaan

Hitung a , b , dan c , jika x → 1 lim x 3 − 3 x + 2 a x 2 + b x + c = 4

Hitung $a, b, dan c$ , jika $x \to 1 lim \frac{a x ^{2} + b x + c}{x ^{3} - 3 x + 2} = 4$

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

nilai .

Pembahasan

Dengan menggunakan konsep limit, diperoleh: Jadi, nilai .

Dengan menggunakan konsep limit, diperoleh:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow 1 of fraction numerator a x squared plus b x plus c over denominator x cubed minus 3 x plus 2 end fraction end cell equals 4 row cell limit as x rightwards arrow 1 of fraction numerator a x squared plus b x plus c over denominator open parentheses x minus 1 close parentheses open parentheses x minus 2 close parentheses end fraction end cell equals 4 row cell Untuk space straight x end cell equals cell 1 comma space bentuk space 0 over 0 space maka colon end cell row cell limit as x rightwards arrow 1 of fraction numerator a x squared plus b x plus c over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis end fraction end cell equals cell 4 space rightwards arrow limit as x rightwards arrow 1 of fraction numerator open parentheses x minus 1 close parentheses open parentheses x plus d close parentheses over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis end fraction equals 4 end cell row blank blank blank row cell limit as x rightwards arrow 1 of fraction numerator left parenthesis x plus d right parenthesis over denominator left parenthesis x minus 2 right parenthesis end fraction end cell equals cell 4 space rightwards arrow 1 plus d equals negative 4 space rightwards arrow d equals negative 3 comma space sehingga end cell row blank blank blank row cell a x squared plus b x plus c end cell equals cell open parentheses x minus 1 close parentheses left parenthesis x minus 3 right parenthesis end cell row blank blank blank row cell a x squared plus b x plus c end cell equals cell x squared minus 4 x plus 3 end cell row blank blank cell a equals 1 comma space b equals negative 4 space dan space c equals 3 end cell end table end style$

Jadi, nilai .